SART算法matlab
时间: 2023-12-14 22:34:09 浏览: 69
以下是SART算法的MATLAB实现示例:
```matlab
function [x, err] = SART(A, b, x0, niter)
% SART - Simultaneous Algebraic Reconstruction Technique
%
% Usage:
% [x, err] = SART(A, b, x0, niter)
%
% Input:
% A - Projection matrix
% b - Measured data
% x0 - Initial guess
% niter - Number of iterations
%
% Output:
% x - Reconstructed image
% err - Error vector
%
% This is a simple implementation of the SART algorithm.
% The algorithm is based on the following update rule:
%
% x_i+1 = x_i + lambda_i * A' * (b - A * x_i)
%
% where lambda_i is the relaxation parameter at iteration i.
% In this implementation, lambda_i is set to 1.
%
% Author: Brendt Wohlberg <brendt@lanl.gov> Modified: 2015-12-29
%
% Get problem dimensions
[m, n] = size(A);
% Initialize variables
x = x0;
err = zeros(niter, 1);
% Loop over iterations
for i = 1:niter
% Loop over projections
for j = 1:m
% Compute relaxation parameter
lambda = 1 / norm(A(j,:))^2;
% Update estimate
x = x + lambda * A(j,:)' * (b(j) - A(j,:) * x);
end
% Compute error
err(i) = norm(A * x - b);end
end
```
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